QQuestion
If A = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, then A² is equal to:
(a) \begin{bmatrix}1 & 1 \\ 0 & 0\end{bmatrix}
(b) \begin{bmatrix}0 & 0 \\ 1 & 1\end{bmatrix}
(c) \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}
(d) \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
✓Answer
(c) \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}
Explanation:
A² = A × A
A² = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
A² = \begin{bmatrix}(0\times0)+(1\times1) & (0\times1)+(1\times0) \\ (1\times0)+(0\times1) & (1\times1)+(0\times0)\end{bmatrix}
A² = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}
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